This is armor designed to be unobtrusive - to be seen as clothing, nothing more. Some regular armor can be concealed under clothing, but these are designed to be invivible in themselves.
In order to protect against energy weapons, this kind of armor has to have a high resistance to radiation, so it is pretty easy to discover undercover armor using sensors. On the other hand, it is usually seen as a fashion statement, so there is rarely any trouble when it is discovered for what it is - merely slightly raised eyebrows.